|Sabertooth has it right in one.|
To expand a little on that, the router will mask the true IP address with one that which it gets from the ISP.
For example: if true IP is 188.8.131.52
Router will show something like: 184.108.40.206
Even better is to compliment the router with a good software firewall that will monitor programs trying to access the net from within.
Sorta like a jail :-)
Router keeps the bad eggs out. Software firewall prevents those that are in from getting out.